How would you prove it's not a P.I.D. by using I?

Let http://www.math.mtu.edu/graduate/comp/img81.gif be an ideal of http://www.math.mtu.edu/graduate/comp/img82.gif. Prove thatIis not a principal ideal of http://www.math.mtu.edu/graduate/comp/img82.gif.

I've been trying this for a long time... and I'm just saying okay it has this form, and then I multiply it by (a+bsqrt(-5)) and this happens... but I keep getting so many terms, that I can't find a contradiction. Please help!